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The constitution and structure of gold-cadmium alloys
THE
CONSTITUTION V.
AND
G.
STRUCTURE
RIVLIN,$
W.
OF
GOLD-CADMIUM
ALLOYS*
and B. RYDERt
HUME-ROTHERYT
The equilibrium diagram of the system Au-Cd has been investigated by thermal, microscopical, and X-ray diffraction m&hods. At high temperatures the phases present are (1) the cc solid solution of cadmium in gold, (2) the CL* phase which is of variable composition with close-packed hexagonal structure, and (3) the p body-centred cubic phase which remains highly ordered at a few degrees below the melting point. No evidence was found for the existence of the a? phase claimed by Owen et al. or of the a” phase postulated by Bystram and Almin, On the cadmium-nch side, the do;phase has a normal close-packed hexagonal sbructure but, in the range 27-34 at. o/0Cd, highly faulted structures are observed, and a possible cause of this is suggested in terms of the curves of densities of electronic states. In the region of 25 at. y0 Cd, at low temperatures, a face-centred tetragonal phase is formed, and also a new face-centred cubic phase which has not been described before. CONSTITUTION
ET STRUCTURE
DES ALLIAGES
OR-CADMIUM
Les auteurs ont &udi6 le diagramme d’bquilibre du systbme Au-Cd, par analyse thermique, par micrographie et par diffraction des rayons X. Les phases presentes B haute temperature sont (1) la solution solide a de cadmium dans l’or (2) la phase cr, qui possede une structure hexagonale compacte et une composition variable et (3) la phase ,!I’, cubique cent&e, qui reste hautement ordonnbe jusqu’8 quelques degr& du point de fusion. Les auteurs n’ont pas observe!la phase as signal& par Owen et al. ni la phase a” admise par Bystram et Almin. Dans le domaine riche en cadmium, la phase a, possede une structure hexagonale compacte normale, mais on observe dans le domaine 27-34 et-% Cd des structures avec une forte proportion de fontes d’empilement, dont l’explication pourrait 6tre trouvt?e dans les courbes de densite Blectronique. Dans le voisinage de 25 at-% Cd, une phase t&ragonale B faces cent&es se forme basse tempbrature, de mhme qu’une nouvelle phase cubique Q faces centrbes qui n’a pas encore BtB d&rite jusqu’8 p&sent. ZUSAMMENSETZUNG
UND
STRUKTUR
VON
GOLD-KADNIUM-LEGIERUNGEN
Das Gleichgewichtsphrtsendiagramm des Systems Au-Cd wurde mit thermischen, mikroskopischen und rijntgenographischen Methoden untersucht. Bei hoher Temperatur liegen folgende Phasen vor: (1) die a-Phase, eine feste L6sung von Kadmium in Gold, (2) die as-Phase mit hexagonal dichtest gepackter Struktur unterschiedlicher Zusammensetzung und (3) die kubisch raumzentrierte B-Phase, die bis wenige Grade unter den Schmelzpunkt stark geordnet bleibt. Die Existenz der von Owen et al. berichteten a,-Phase und der von BystrBm und Almin geforderten a”-Phase konnte nicht nachgewiesen werden. Auf der kadmiumreichen Seite hat die a,-Phase normale hexagonal dichtest gepackte Struktur, im Bereich von 27-34 Atom% Cd werden dagegen stark fehlerhafte Strukturen beobachtet, deren mBgliche Ursache wohl im Verlauf der Elektronenzustandsdichten eu suchten ist. Im Bereich urn 25 Atom% Cd wird bei tiefen Temperaturen sine tetragonale fl5chenzentrierte Phase gebildet, auIjerdem noch eine neue kubisch fl&chenzentriertePhase, die friiher noch nicht angegeben wurde.
I. INTRODUCTION
The
equilibrium
AND
PREVIOUS
diagram
of
as given by Hansen(l)
cadmium
the
WORK
system
rhombohedral
gold-
is shown in Fig. 1.
Owing mainly to the work of DurrantP) the cadmiumFor the gold-
widely,
and the following
(1) The B’-phase but, according
investigators
(3) The
differ
structure
points may be noted:
has an ordered
to the calorimetric
b.c.c.
by
structure
Owen
formation
work of Kubaschew-
skid3), the phase becomes disordered
This work was carried out on
the high-temperature Almin.c6)
half of the diagram is well established. rich part, the results of different
chart.
quenched filings, and the a,-phase was not detected
started,
at high tempera-
as-phase whose
X-ray
in and
in Fig. 1 has a c.p. hexagonal
was unknown the
of Bystrijm
phase-boundaries
et al. (Eoc. cit.). and
work
The
were determined mechanism
of its
when the present work was
625°C.
peritectic
horizontal
was
included merely to fit the phase into the diagram.
tures. At low temperatures, alloys on the gold-rich and cadmium-rich sides of this phase undergo trans-
(4) The solubility limits of the a-solid solution of cadmium in gold were determined between 300°C
formations
and 550°C by the X-ray
to orthorhombic
respectively; able.
and tetragonal
these structures
The low temperature
are probably
changes
structures metast-
have been con-
formation
firmed, but not studied in the present work. (2) According to Owen et uZ.(~*~),the /l’-phase on the gold-rich side is in equilibrium with an a,-phase, most
of
whose
diffraction
lines
fit
a hexagonal-
* Received March 12, 1962. t Department of Metallurgy, Oxford University. # Now at the Fulmer Research Institute, Stoke Pages, Bucks. ACTA METALLURGICA,
VOL. 10, DECEMBER
1962
work of Owen et al. (lot. cit.).
The change in direction at 425°C (Fig. 1) is due to the of the al-phase
by a peritectoid
reaction;
according to Hirabayashi and 0gawac7) this reaction occurs at 412%, whilst Kijster and Schneider(s) place it at 415°C. (5) The al-phase has a face-centered tetragonal structure, and according to Owen et al. (Zoc. cit.) this does not give rise to superlattice lines, although these were observed by Bystram and Almin (Zoc. cit.) who
1143
1144
ACT4
METALLURGICA, Weight
per cent
VOL.
10,
1962
cadmuim
Flu. 1. The equilibrium diagram of the system gold-cadmium taken from Constitution of Binary Alloys, by M. Hansen. Copyright (1958). McGraw-Hili Book Company, Iuc, Used by permis8ion. The phase oalled fl in the diagram is called ,9’ in the text.
also postulated the existence of a further a” phase above 425°C. II. EXPERIMENTAL
METHODS
The gold used in the present work was supplied by Messrs. Johnson, Hathey t Co., Limited, whilst the cadmium was kindly presented by the Imperial Smelting Corporation, The purity of both metals exceeded 99.99 %. The liquidus curve was determined by means of cooling curves, using ingots of ca. 20 g. melted under graphite in graphite crucibles, provided with graphite lids through which holes were drilled to admit a thin silica thermocouple sheath and stirrer. The rate of cooling was of the order lo-2’/min at the arrest point, and alI the precautions* customary in the authors’ laboratory were taken. All ingots were analysed chemically, and the results showed that very little loss * For some of these details see: “Metallurgical Equilibrium
Diagrams” by W. Hume-Rothery, J. W. Christian, and W. B. Pe&rson.
of cadmium occurred, and that the ingots were satisfactorily pure. For the determination of the solidus curves and of the phase boundaries in the solid state, alloys were prepared by melting the constituent metals in sealed silica tubes which were either evacuated, or Wed with argon at low pressure. After thorough mixing of the constituents, the tubes were quenched into water or iced brine. The sohdus curve was determined by the conventional method of quenching previously homogenized specimens from successive temperatures,? followed by microscopical examination for the presence of chilled liquid. For the determination of structures below the solidus, specimens were annealed in sealed evacuated tubes in controlled furnaces, and were then quenehed and examined microscopically after preparation by standard methods, and chemical etching in aqua regia t In this work the temperature was controlled by hand to within &O.?‘“C of the desired value except on a few occasions when the variation was f l.O"C. With the temperature controllers, the constancy was within the 1imit.s 13°C.
RIVLKN,
HUME-ROTHERY
AND
.RYDER:
or electrolytic etching in very dilute aqueous hydrochloric acid. The times of annealing varied from 24 hr at GOO”C,to 3 months at 24O”C, and 8 months at 150°C. The X-ray diffraction experiments at room temperatures were carried out by powder methods in a 9 cm Hilger camera. In general, alloys were annealed to equilibrium in lump form, quenched, and filed, after which the filings were strain-annealed at the same temperature. For the high temperature work the specimens were contained in sealed silica capillaries, and use was made of a 19 cm Unicam camera with modified furnaces, and the thermoeoup~es were calibrated by measuring the lattice spacings of pure silver, for which the lattice spacing/temperature relation is known (Pearson(Q)). Standard extrapolation techniques were used throughout, The compositions of the alloys were taken to be those calculated from the weights of metals melted together, on the assumption that any very slight loss was that of cadmium. This method of preparation has been tested and found satisfactory in several other systems. III.
THE
LIQUIDUS
AND SOLIDUS
The results of the cooling curve experiments are shown in Table 1, and are plotted in Fig. 2 which also inoludes the solidus points.
t
I
20
30
GOLD-CADMIUM TABLE
Atomic
l/o Cd
&rest
10.40 19.86 29.61 34.64 35.29 39.14
40.10
40.19 41.08 41.7Q 42.76 43.93 44.54 45.78 46.80 47 34 51:02 5 1.53 54.22
1.
.._.,
temperature -._--___ ____ 971.5 873.1 768.2 709.3 627.3 702.4 627.0 650 627.1 626.6 626.4 626.2 626.3 626.6 6265 626.6 626.6 627.3 627.6 627.1 628.8 628.8 628.9 628.7 627.6 621.4 603.9
L = Liquidus, P = Periteotic, E = Eutectic, H = Heating Curve, C = Cooling Curve. * These arrests were pronounced and extended in contrast to the horizontal eutectic arrests.
equilibrium
diagram
of the system
:
Notes
PC LC PC LC PC EC 0*
H*
EC EC EC EH EC
::: SH LC SH LC LC 132 LC LC S = Solidus, over lo-2’,
The addition of cadmium to gold produces a fall in the liquidus and solidus curves, and a eutectic point
I
40
t
50
I
60
Atoatk vcr cent Cadmhtm Fro. 2. The
1148
ALLOYS
gold-cadmium
in the region O-50 at. T/o cadmium.
1146
ACTA
METALLURGICA,
exists at 626.6% and between 42 and 43 at. % Cd, this composition being established by thermal analysis and by the microstructures of cooling curve ingots. Ideally horizontal thermal arrests were obtained for alloys slightly to the gold-rich side of the eutectic but, on moving to somewhat higher gold contents, the arrests, although pronounced, extended over a slight range of temperature. It is concluded that a second horizontal exists at from 0.5-1.0% above the eutectic horizontal, and that this new horizontal corresponds to the (a + Liq + as) peritectic reaction. This interpretation was confirmed by the fact that a hightemperature X-ray diffraction film of alloy 35.7* taken just above the melting point showed lines from the c.p. hexagonal a2 phase, whereas a film of the same alloy at 634°C showed lines of the f.c.c. a-phase; both these films showed a few very faint unidentified lines. With increasing cadmium content, the liquidus and solidus rise to a flat maximum at 629°C and about 46 at. % Cd. The two curves remain very close together until 50 at. y0 Cd, beyond which both begin to fall, and become more widely separated.
VOL.
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1962
become broad and diffuse, and the film appears at first sight to be that of a f.c.c. structure with a few lines missing, and an extra line at the high angle end. Measurement showed the remaining lines to be those of a close-packed hexagonal structure for which (h - k) is divisible by 3, and the facts are consistent with the presence of heavily faulted structures which persist
IV. THE NON-EXISTENCE OF THE SUPPOSED as- AND cd’ PHASES
In spite of numerous tests by thermal analysis, microscopy, and high temperature X-ray diffraction, no evidence could be found for the existence of the Q-phase claimed by Owen et al. (Zoc. cit.). The supposed aJa2 + a3 and as + as/% phase boundaries given by these authors are very near to the as/a2 + fi’ and a2 + p’/@’ b oundaries of the present work. The present conclusion agrees with that of Bystrom and Almin (Zoc. cit.), and it aeems almost certain that the results of Owen et al. were vitiated by decomposition of the p’-phase during quenching. No evidence was found for the existence of the a” phase proposed by Bystrijm and Almin (Zoc. cit.). V.
THE
q-PHASE
The results obtained for the as-phase were of great interest. For compositions in the middle and cadmiumrich side of the as-phase field, the X-ray diffraction films at both high and room temperatures showed sharp lines for all the reflections to be expected from a normal close-packed hexagonal structure. On reducing the cadmium content below about 34 at. %, some lines began to drop out of the diffraction picture, whilst others became extremely diffuse. Fig. 3 shows the powder diffraction film of alloy 28 at 299.3%. Here, most of the lines have either disappeared, or * For abbreviation, alloys are referred to by their cadmium
contents in at. %.
FIG. 3. X-ray powder diffraction film of the 28 at. “/b cadmium alloy at 299.3% The pattern is that of a close-packed hexagonal structure with heavy faulting.
RIVLIN,
HUME-ROTHERY
AND
RYDER:
a,sfar back as 27 at. ‘A Cd. In the homogeneous alloys, there was no convincing evidence for the existence of the structure with ABACABAC . . . . packing suggested by Hirabayashi and Ogawa (lot. tit). For the 2:phase (f.c.c. + c.p.h.) alloys the diffraction patterns contain a few extra unidentified lines, of which some might fit the double cell of H. and O., whilst others woula not. Visual comparison of the powder films suggests that the faulting process is not greatly affected by the temperature, but depends essentially on the composition, and it seems that, with increasing gold content, the stability of the normal close-packed hexagonal structure begins to decrease rapidly when the ratio Au atoms: Cd atoms exceeds about 2:l (see p. 1148). The faulting reaches a maximum at about 27 at. % Cd, and on passing to 26 at. ‘A Cd the structures of the alloys below 400°C become (f.c.c. + c.p.h.) with sharp diffraction lines, and no indication of faulting (see Section VII below). Correspondence with Professor E. A. Owen showed that in the work by Owen and Robertsc4) diffraction patterns of faulted structures were not observed. In order to see whether this discrepancy was due to the method of preparation of the specimens, an alloy containing approximately 28 at. % Cd was prepared by interdiffusion of the two metals, as in the work of Owen and Roberts. A sample of this material when photographed at 390°C in the high temperature camera gave the typical diffraction pattern of a faulted structure. It is not possible to say why Owen and Roberts did not observe this effect. There is some evidence that, with prolonged annealing in the high temperature camera, the diffuse lines begin to separate into sharper components. VI.
THE
ORDERED
P-PHASE
The us + p’/p’ b oundary determined in the present work is shown in Fig. 2, and the high temperature X-ray films showed conclusively that the ordered @‘-phase is in equilibrium with the as close-packed hexagonal phase. The @‘I/?’ + y boundary in Fig. 2 is that of Owen et al. (Zoc. cit.), and agrees with the present data. High temperature X-ray work showed alloy 47.7 to be highly ordered just below the melting point. From the measured integrated intensities of the (100) superlattice and (110) main lattice lines, the degree of ordering of this alloy was calculated to be approximately 90 per cent at 620°C. The calculation was made on the assumption of an equiatomic alloy, and without correction for the temperature or absorption factors. The errors due to these two factors tend to compensate for each other, and the calculated value
GOLD-CADMIUM
ALLOYS
1147
is thus approximately correct, and suggests strongIy that Kubaschewski’s conclusion (p. 1143) was in error. VII. CONSTITUTION IN THE REGION
AND 25 at.
STRUCTURES
y0 CADMIUM
Owing to the difficulty of obtaining true equilibrium in this region, most of the high-temperature X-ray work was carried out on specimens which had previously been homogenized for 11 weeks at 351°C and were then heated for an hour or more at the required temperature in the X-ray camera before the exposure was started. Other experiments were made with a shorter preliminary anneal and a longer period (up to 48 hr) in the camera. In agreement with previous workers, the a,-phase was found to be face-centred tetragonal, the axial ratio being > 1.0, and decreasing with increasing Cd content. For any given composition, the axial ratio decreases with rise of temperaure, but does not become equal to unity at the (a + a,)/al boundary. The a,-phase boundary limits are shown in Fig. 2,* and on the Cd-rich side the a,-phase extends to about 24 at. % Cd. At slightly higher Cd-contents a f.c.c. phase appears. The high temperature X-ray films could be reconciled with a continuous change from face-centred tetragonal --f f.c.c. with increasing Cd content, but since a change in symmetry is involved, it is probable7 that a S-phase field exists between the tetragonal and cubic phases, and this is confirmed by the fact that the axial ratio/composition data of Owen and Roberts (Zoc.cit.) do not extrapolate to unity inside the al-field. The form of the equilibrium diagram in this region is difficult to establish. Since heavy faulting is present, it may be argued that true thermodynamic equilibrium is never obtained. In this case the region between the f.c.c. and a2 phases should be left as an indefinite field, about 2 at. % in width. In so far as the results of this, and the earlier work may be used, we think that the most probable form of the equilibrium diagram is that of Fig. 2. This is based on more than 100 high-temperature X-ray exposures in the range 20-34 at. % Cd.: Independent work by two of the present authors (V. G. R. and B. R.) using completely different alloys, established the existence of the f.c.c. a,-phase which is shown as undergoing a peritectoidal decomposition at 412°C this temperature being taken from the work * The interplanar spacingsof the a and a, phases are nearly the same and one criterion for a single phase a1 alloy is that the (222) line remains sharp. t We have to thank Dr. J. W. Christian for discussion on this point. $ For clarity of reproduction, the individual points are not shown in Fig. 2.
1148
ACTS
~~ETALLUR~IC~~,
t T
“C
Cadmium
+
Fra. 4. To illustrate a possible form of the equilibrium diagram in the region of 25 at. y0 cadmium. As explained in the text this does not appear to account for all the facts.
Hirabayshi and OgawaQ) on the basis of a carefully determined specific heat~~mperature curve of an alloy oontaining 24 at. a/0Cd, which they regarded as undergoing an order-disorder change, followed by the periteotoidal decomposition. The present authors concluded independently that this transformation is at a lower temperature than the previously accepted value (425%). On the Cd-rich side the existence of a f.c.0. phase suggests another peritectoidal horizontal. This may be placed at 407”C, at which temperature* H. and 0. observed a pronounced narrow peak on their specific heatl~mperature curve. The present results could be reconciled with a diagram of the type of Fig. 4, but this would lead to greater difficulties in interpreting H. and 0.‘~ data. The Cd-rich limit of the new f.c.c. a’ phase is placed at about 25 at. % Cd, in agreement with which 26 at. %Cd alloys prepared from different ingots gave 2-phase (f.c.c. + c.p.h,) diffraction films at the lower temperatures. One nominally 25 at. % Cd alloy gave a f.c. tetragonal diffraction pattern, and it is possible that slight loss of cadmium by volatilization occurred, because another 25 at.‘% Cd alloy gave a f.c.c diffraction pattern with very slight traces of c.p. hexagonal lines. of
DISCUSSION
(a) Liquih
curves of gold a1hy.s with ml&s
ofgroup II
It has previously been pointed out that, in the electrochemical series, gold is more electronegative * H. and 0, interpreted their data as indicating that the alloy in question had crossed a phase-boundary. The pronounced nature of the arrest suggests, however, that it was due to a true latent heat of transformation for which the experimental conditions did not allow an infinite specific heat to be detected.
VOL.
10,
1962
than copper or silver. The concept of an “eleotrochemical factor” has frequently been used in alloy theory but is difficult to define precisely, because the standard electrode potentials refer to equilibrium between a metal and an aqueous solution of its ions, whilst the Pauling ““electronegativities” are in reality bond energy terms derived from non-metallic compounds. If, as in the Pauling hypothesis (see Pauling’lO)), the metallic bond is regarded as a kind of unsaturated co-valent bond, the Pauling electronegativities are perhaps the least unsatisfactory measure of the ‘~ele~trochemical factor”. Pig. 5 shows the liquidus curves for the alloys of silver and gold with the solutes of group IIB for which the size factors are all favourab1e.t The figure indicates the difference, Ax, between the electronegativities of solvent and solute, and the general effect of increasing Ax in raising the liquidus curves is clear. In the systems Ag- Zn and Au- Zn the size-factor is - 7 per cent (i.e. the solute atom is smaller than that of the solvent) and it may be for this reason that the a-liquidus curves fall relatively steeply in these systems. In the remaining sys~ms the size-factor is very favourable, and the a-liquidus curves for Ag-Mg and Au-Mg fall the least steeply of their respective series. These are the systems with the highest Ax values, and the diagrams suggest that the high electrochemical factor stabilizes the solid phase, presumably by the production of the short-range order. A high electrochemical factor also stabilizes the intermediate solid phases with respect to the liquid. This effect is particularly marked for equiatomic b.c.c. phases with the C&l structure, presumably because each atom is surrounded by 8 of the opposite kind. It is probably because of the great stability of this phase in the systems Au-Mg and Au-&r that closepacked hexagonal phases analogous to the Au-Cd as-phase are not found in these systemsf (b) The cl2close-packed hexagonal phases The characteristic of the a2 close-packed hexagonal phase is the occurrence of severe stacking faulting when the cadmium content is less than about 1 atom in 3. It does not seem possible to account for this on the assumption that, by means of an ordered structure the close-packed hexagonal stacking of spheres can keep the Cd atoms further away from one another than the f.c.c. close-packing, It is possible that Brillouin t A corresponding diagram cannot be drawn for copper, because the size-factors are unfavourable except for CuZn. $ If the free-energy curve of the p phase is sufficiently low, the tangent of this and the f.c.c. curve may pass below the curve for a close-packed hexagonal phase of the a,AuCd type.
RIVLIN,
-.
HUME-ROTHERY
AND
RYDER:
COLD-CADMIUM
b-9
Ax=0.0
Ag-CI
Ax-O.2
Ag-Zn
Ax-O.3
Au- Hq
&u-O5
Au- Cd
Ax-O-7
Au-Zn
Ax-O.8
ALLOYS
Ag-Mq
1149
Ax=0 7
‘\ LX I\ \\ \\
‘--,...
*.-.. FIG. 5. Liquidus
curves of some silver and gold alloys.
zone e&&s may a.ccount for the phenomenon in the following way : It is commonly stated (see Raynor and ~assa~ki(ll)) that with an axial ratio of 1.633 (spherical close packing) a spherical Fermi surface touches the A, B, and C faces of the Jones’ zone (Fig. 6) at electron concentrations of 1.14, 1.36, and 1.67 respectively, but this is incorrect if energy gaps exist, and it is only if such gaps exist that Brillouin zones can exert any effect on alloy structures. The value 1.36 for contact with the B faces is the same as that for contact with the octahedral faces of the first Brillouin zone for the f.c.c. structure, because each corresponds to the same interplanar spacing. But with the close-packed hexagonal structure, the initial contaot with the A faces of the zone means that electron states are cut out, until the zone overlap occurs. The correct statement is, therefore, that: Contact with the A faces of the zone occurs at e.c. 1.14 if the Fermi surface is spherical.
Contact with the B faces occurs at e.c. 1.36 minus an amount which may vary from zero for a zero energy gap at the A faces, to a value corresponding to the volume of 6 spherical caps outside the A faces which have not been occupied because of the energy gaps. Contact of a spherical Fermi surface with the C faces of zone occurs at an electron concentration of 1.67 minus corresponding correction for the effects of the energy gaps at the A and B faces. If the overlap across the A faces occurs before the Fermi surface (assumed spherical) reaches the B faces, the N(E) curve will be of the form of Fig, 7, whereas if the energy gap at the A faces is su~ciently large, the N(E) curve will be of the form of Fig. 8. These curves clearly give the possibility of a region in which the energies of the f.e.c. and close-packed hexagonal structures are nearly the same, whereas with increasing electron concentration the close-packed structure may be stabilized. It does not seem justifiable to speculate further until more is known of the energy gaps and of the distortion of the Fermi surfaces in the alloys.
E
Pm. 6. The
first
Jones’ zone for the hexagonal structure.
close-packed
FIG. 7. Possible X(E) curves for face-centred cubic and close-packed hexagonal structures. For the latter, the energy gaps at the zone faces are assumed to be so small that zone overlaps occur.
1150
ACTA
~~ETALLURGICA,
VOL.
10,
1962
Oriel College, Oxford, for a research grant. The authors alsoexpress their thanks to the Council of the Royal Society and Imperial Chemical Industries Limited for financial assistance towards the present research. Thanks are also due to Dr. A. Hellawell for much valuable discussion. REFERENCES
E FIU. 8. Possible Nfgf curves for face-centred cubic and close-psoked hexsgonsl structures. For the latter, the energy gaps sre assumed to be so large that no overlapping has occurred while the Fermi surface sprea,ds out to contact with the zone faces at A, B, and C.-The ourves are schematic only, and sre not drswn to scale. ACKNOWLEDGMENTS
One of the authors (V. G. R.) acknowledges with gratitude the award of a D.S.I.R. Research Studentshin, A, whilst another (B. It.) thanks the Fellows of
1. M. RAESEE, Constdt&ioon of Binary Alloys McGEAw-HILL, New York (1958). 2. P. J. DTI’RRANT, J. Inst. MetaL. 41, 139 (1929). 3. 0. KUBASCHEWSEI,Z. p&s. China. 192, 292 (1943). 4. E. A. OWEN and E, A. O’DONNELL R.OBERTS,J. f?a& beak. 66, 389 (1.940). 5. E. A. OWEN and W. H. REES, J. Inst. Metals. 67, 141 (1941). 6. A. BYSTRBMand K. E. ALMIN, Acta them. scmd. 1, ‘76 (1947). 7. M. HIRABAYSRIsnd S. OQAWA, Actu Met. 9, 264 (1961). 8. W. KGSTERand A. SCXNEIDER,2. Metallk. 32, 156 (1940). 9. W. B. PEARSON, Handbook of Lattice i9pacings ad Structures of Metals, Pergamon Press, London (1968). 10. L. PAULINQ, The Nature of the Chemical Bond, Oxford University Press ( 1960). 11. G. V. RAYNOR and T. B. MASS&S~I, Ada Met. 8, 480 (1955).
CONSTITUTION V.
AND
G.
STRUCTURE
RIVLIN,$
W.
OF
GOLD-CADMIUM
ALLOYS*
and B. RYDERt
HUME-ROTHERYT
The equilibrium diagram of the system Au-Cd has been investigated by thermal, microscopical, and X-ray diffraction m&hods. At high temperatures the phases present are (1) the cc solid solution of cadmium in gold, (2) the CL* phase which is of variable composition with close-packed hexagonal structure, and (3) the p body-centred cubic phase which remains highly ordered at a few degrees below the melting point. No evidence was found for the existence of the a? phase claimed by Owen et al. or of the a” phase postulated by Bystram and Almin, On the cadmium-nch side, the do;phase has a normal close-packed hexagonal sbructure but, in the range 27-34 at. o/0Cd, highly faulted structures are observed, and a possible cause of this is suggested in terms of the curves of densities of electronic states. In the region of 25 at. y0 Cd, at low temperatures, a face-centred tetragonal phase is formed, and also a new face-centred cubic phase which has not been described before. CONSTITUTION
ET STRUCTURE
DES ALLIAGES
OR-CADMIUM
Les auteurs ont &udi6 le diagramme d’bquilibre du systbme Au-Cd, par analyse thermique, par micrographie et par diffraction des rayons X. Les phases presentes B haute temperature sont (1) la solution solide a de cadmium dans l’or (2) la phase cr, qui possede une structure hexagonale compacte et une composition variable et (3) la phase ,!I’, cubique cent&e, qui reste hautement ordonnbe jusqu’8 quelques degr& du point de fusion. Les auteurs n’ont pas observe!la phase as signal& par Owen et al. ni la phase a” admise par Bystram et Almin. Dans le domaine riche en cadmium, la phase a, possede une structure hexagonale compacte normale, mais on observe dans le domaine 27-34 et-% Cd des structures avec une forte proportion de fontes d’empilement, dont l’explication pourrait 6tre trouvt?e dans les courbes de densite Blectronique. Dans le voisinage de 25 at-% Cd, une phase t&ragonale B faces cent&es se forme basse tempbrature, de mhme qu’une nouvelle phase cubique Q faces centrbes qui n’a pas encore BtB d&rite jusqu’8 p&sent. ZUSAMMENSETZUNG
UND
STRUKTUR
VON
GOLD-KADNIUM-LEGIERUNGEN
Das Gleichgewichtsphrtsendiagramm des Systems Au-Cd wurde mit thermischen, mikroskopischen und rijntgenographischen Methoden untersucht. Bei hoher Temperatur liegen folgende Phasen vor: (1) die a-Phase, eine feste L6sung von Kadmium in Gold, (2) die as-Phase mit hexagonal dichtest gepackter Struktur unterschiedlicher Zusammensetzung und (3) die kubisch raumzentrierte B-Phase, die bis wenige Grade unter den Schmelzpunkt stark geordnet bleibt. Die Existenz der von Owen et al. berichteten a,-Phase und der von BystrBm und Almin geforderten a”-Phase konnte nicht nachgewiesen werden. Auf der kadmiumreichen Seite hat die a,-Phase normale hexagonal dichtest gepackte Struktur, im Bereich von 27-34 Atom% Cd werden dagegen stark fehlerhafte Strukturen beobachtet, deren mBgliche Ursache wohl im Verlauf der Elektronenzustandsdichten eu suchten ist. Im Bereich urn 25 Atom% Cd wird bei tiefen Temperaturen sine tetragonale fl5chenzentrierte Phase gebildet, auIjerdem noch eine neue kubisch fl&chenzentriertePhase, die friiher noch nicht angegeben wurde.
I. INTRODUCTION
The
equilibrium
AND
PREVIOUS
diagram
of
as given by Hansen(l)
cadmium
the
WORK
system
rhombohedral
gold-
is shown in Fig. 1.
Owing mainly to the work of DurrantP) the cadmiumFor the gold-
widely,
and the following
(1) The B’-phase but, according
investigators
(3) The
differ
structure
points may be noted:
has an ordered
to the calorimetric
b.c.c.
by
structure
Owen
formation
work of Kubaschew-
skid3), the phase becomes disordered
This work was carried out on
the high-temperature Almin.c6)
half of the diagram is well established. rich part, the results of different
chart.
quenched filings, and the a,-phase was not detected
started,
at high tempera-
as-phase whose
X-ray
in and
in Fig. 1 has a c.p. hexagonal
was unknown the
of Bystrijm
phase-boundaries
et al. (Eoc. cit.). and
work
The
were determined mechanism
of its
when the present work was
625°C.
peritectic
horizontal
was
included merely to fit the phase into the diagram.
tures. At low temperatures, alloys on the gold-rich and cadmium-rich sides of this phase undergo trans-
(4) The solubility limits of the a-solid solution of cadmium in gold were determined between 300°C
formations
and 550°C by the X-ray
to orthorhombic
respectively; able.
and tetragonal
these structures
The low temperature
are probably
changes
structures metast-
have been con-
formation
firmed, but not studied in the present work. (2) According to Owen et uZ.(~*~),the /l’-phase on the gold-rich side is in equilibrium with an a,-phase, most
of
whose
diffraction
lines
fit
a hexagonal-
* Received March 12, 1962. t Department of Metallurgy, Oxford University. # Now at the Fulmer Research Institute, Stoke Pages, Bucks. ACTA METALLURGICA,
VOL. 10, DECEMBER
1962
work of Owen et al. (lot. cit.).
The change in direction at 425°C (Fig. 1) is due to the of the al-phase
by a peritectoid
reaction;
according to Hirabayashi and 0gawac7) this reaction occurs at 412%, whilst Kijster and Schneider(s) place it at 415°C. (5) The al-phase has a face-centered tetragonal structure, and according to Owen et al. (Zoc. cit.) this does not give rise to superlattice lines, although these were observed by Bystram and Almin (Zoc. cit.) who
1143
1144
ACT4
METALLURGICA, Weight
per cent
VOL.
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1962
cadmuim
Flu. 1. The equilibrium diagram of the system gold-cadmium taken from Constitution of Binary Alloys, by M. Hansen. Copyright (1958). McGraw-Hili Book Company, Iuc, Used by permis8ion. The phase oalled fl in the diagram is called ,9’ in the text.
also postulated the existence of a further a” phase above 425°C. II. EXPERIMENTAL
METHODS
The gold used in the present work was supplied by Messrs. Johnson, Hathey t Co., Limited, whilst the cadmium was kindly presented by the Imperial Smelting Corporation, The purity of both metals exceeded 99.99 %. The liquidus curve was determined by means of cooling curves, using ingots of ca. 20 g. melted under graphite in graphite crucibles, provided with graphite lids through which holes were drilled to admit a thin silica thermocouple sheath and stirrer. The rate of cooling was of the order lo-2’/min at the arrest point, and alI the precautions* customary in the authors’ laboratory were taken. All ingots were analysed chemically, and the results showed that very little loss * For some of these details see: “Metallurgical Equilibrium
Diagrams” by W. Hume-Rothery, J. W. Christian, and W. B. Pe&rson.
of cadmium occurred, and that the ingots were satisfactorily pure. For the determination of the solidus curves and of the phase boundaries in the solid state, alloys were prepared by melting the constituent metals in sealed silica tubes which were either evacuated, or Wed with argon at low pressure. After thorough mixing of the constituents, the tubes were quenched into water or iced brine. The sohdus curve was determined by the conventional method of quenching previously homogenized specimens from successive temperatures,? followed by microscopical examination for the presence of chilled liquid. For the determination of structures below the solidus, specimens were annealed in sealed evacuated tubes in controlled furnaces, and were then quenehed and examined microscopically after preparation by standard methods, and chemical etching in aqua regia t In this work the temperature was controlled by hand to within &O.?‘“C of the desired value except on a few occasions when the variation was f l.O"C. With the temperature controllers, the constancy was within the 1imit.s 13°C.
RIVLKN,
HUME-ROTHERY
AND
.RYDER:
or electrolytic etching in very dilute aqueous hydrochloric acid. The times of annealing varied from 24 hr at GOO”C,to 3 months at 24O”C, and 8 months at 150°C. The X-ray diffraction experiments at room temperatures were carried out by powder methods in a 9 cm Hilger camera. In general, alloys were annealed to equilibrium in lump form, quenched, and filed, after which the filings were strain-annealed at the same temperature. For the high temperature work the specimens were contained in sealed silica capillaries, and use was made of a 19 cm Unicam camera with modified furnaces, and the thermoeoup~es were calibrated by measuring the lattice spacings of pure silver, for which the lattice spacing/temperature relation is known (Pearson(Q)). Standard extrapolation techniques were used throughout, The compositions of the alloys were taken to be those calculated from the weights of metals melted together, on the assumption that any very slight loss was that of cadmium. This method of preparation has been tested and found satisfactory in several other systems. III.
THE
LIQUIDUS
AND SOLIDUS
The results of the cooling curve experiments are shown in Table 1, and are plotted in Fig. 2 which also inoludes the solidus points.
t
I
20
30
GOLD-CADMIUM TABLE
Atomic
l/o Cd
&rest
10.40 19.86 29.61 34.64 35.29 39.14
40.10
40.19 41.08 41.7Q 42.76 43.93 44.54 45.78 46.80 47 34 51:02 5 1.53 54.22
1.
.._.,
temperature -._--___ ____ 971.5 873.1 768.2 709.3 627.3 702.4 627.0 650 627.1 626.6 626.4 626.2 626.3 626.6 6265 626.6 626.6 627.3 627.6 627.1 628.8 628.8 628.9 628.7 627.6 621.4 603.9
L = Liquidus, P = Periteotic, E = Eutectic, H = Heating Curve, C = Cooling Curve. * These arrests were pronounced and extended in contrast to the horizontal eutectic arrests.
equilibrium
diagram
of the system
:
Notes
PC LC PC LC PC EC 0*
H*
EC EC EC EH EC
::: SH LC SH LC LC 132 LC LC S = Solidus, over lo-2’,
The addition of cadmium to gold produces a fall in the liquidus and solidus curves, and a eutectic point
I
40
t
50
I
60
Atoatk vcr cent Cadmhtm Fro. 2. The
1148
ALLOYS
gold-cadmium
in the region O-50 at. T/o cadmium.
1146
ACTA
METALLURGICA,
exists at 626.6% and between 42 and 43 at. % Cd, this composition being established by thermal analysis and by the microstructures of cooling curve ingots. Ideally horizontal thermal arrests were obtained for alloys slightly to the gold-rich side of the eutectic but, on moving to somewhat higher gold contents, the arrests, although pronounced, extended over a slight range of temperature. It is concluded that a second horizontal exists at from 0.5-1.0% above the eutectic horizontal, and that this new horizontal corresponds to the (a + Liq + as) peritectic reaction. This interpretation was confirmed by the fact that a hightemperature X-ray diffraction film of alloy 35.7* taken just above the melting point showed lines from the c.p. hexagonal a2 phase, whereas a film of the same alloy at 634°C showed lines of the f.c.c. a-phase; both these films showed a few very faint unidentified lines. With increasing cadmium content, the liquidus and solidus rise to a flat maximum at 629°C and about 46 at. % Cd. The two curves remain very close together until 50 at. y0 Cd, beyond which both begin to fall, and become more widely separated.
VOL.
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1962
become broad and diffuse, and the film appears at first sight to be that of a f.c.c. structure with a few lines missing, and an extra line at the high angle end. Measurement showed the remaining lines to be those of a close-packed hexagonal structure for which (h - k) is divisible by 3, and the facts are consistent with the presence of heavily faulted structures which persist
IV. THE NON-EXISTENCE OF THE SUPPOSED as- AND cd’ PHASES
In spite of numerous tests by thermal analysis, microscopy, and high temperature X-ray diffraction, no evidence could be found for the existence of the Q-phase claimed by Owen et al. (Zoc. cit.). The supposed aJa2 + a3 and as + as/% phase boundaries given by these authors are very near to the as/a2 + fi’ and a2 + p’/@’ b oundaries of the present work. The present conclusion agrees with that of Bystrom and Almin (Zoc. cit.), and it aeems almost certain that the results of Owen et al. were vitiated by decomposition of the p’-phase during quenching. No evidence was found for the existence of the a” phase proposed by Bystrijm and Almin (Zoc. cit.). V.
THE
q-PHASE
The results obtained for the as-phase were of great interest. For compositions in the middle and cadmiumrich side of the as-phase field, the X-ray diffraction films at both high and room temperatures showed sharp lines for all the reflections to be expected from a normal close-packed hexagonal structure. On reducing the cadmium content below about 34 at. %, some lines began to drop out of the diffraction picture, whilst others became extremely diffuse. Fig. 3 shows the powder diffraction film of alloy 28 at 299.3%. Here, most of the lines have either disappeared, or * For abbreviation, alloys are referred to by their cadmium
contents in at. %.
FIG. 3. X-ray powder diffraction film of the 28 at. “/b cadmium alloy at 299.3% The pattern is that of a close-packed hexagonal structure with heavy faulting.
RIVLIN,
HUME-ROTHERY
AND
RYDER:
a,sfar back as 27 at. ‘A Cd. In the homogeneous alloys, there was no convincing evidence for the existence of the structure with ABACABAC . . . . packing suggested by Hirabayashi and Ogawa (lot. tit). For the 2:phase (f.c.c. + c.p.h.) alloys the diffraction patterns contain a few extra unidentified lines, of which some might fit the double cell of H. and O., whilst others woula not. Visual comparison of the powder films suggests that the faulting process is not greatly affected by the temperature, but depends essentially on the composition, and it seems that, with increasing gold content, the stability of the normal close-packed hexagonal structure begins to decrease rapidly when the ratio Au atoms: Cd atoms exceeds about 2:l (see p. 1148). The faulting reaches a maximum at about 27 at. % Cd, and on passing to 26 at. ‘A Cd the structures of the alloys below 400°C become (f.c.c. + c.p.h.) with sharp diffraction lines, and no indication of faulting (see Section VII below). Correspondence with Professor E. A. Owen showed that in the work by Owen and Robertsc4) diffraction patterns of faulted structures were not observed. In order to see whether this discrepancy was due to the method of preparation of the specimens, an alloy containing approximately 28 at. % Cd was prepared by interdiffusion of the two metals, as in the work of Owen and Roberts. A sample of this material when photographed at 390°C in the high temperature camera gave the typical diffraction pattern of a faulted structure. It is not possible to say why Owen and Roberts did not observe this effect. There is some evidence that, with prolonged annealing in the high temperature camera, the diffuse lines begin to separate into sharper components. VI.
THE
ORDERED
P-PHASE
The us + p’/p’ b oundary determined in the present work is shown in Fig. 2, and the high temperature X-ray films showed conclusively that the ordered @‘-phase is in equilibrium with the as close-packed hexagonal phase. The @‘I/?’ + y boundary in Fig. 2 is that of Owen et al. (Zoc. cit.), and agrees with the present data. High temperature X-ray work showed alloy 47.7 to be highly ordered just below the melting point. From the measured integrated intensities of the (100) superlattice and (110) main lattice lines, the degree of ordering of this alloy was calculated to be approximately 90 per cent at 620°C. The calculation was made on the assumption of an equiatomic alloy, and without correction for the temperature or absorption factors. The errors due to these two factors tend to compensate for each other, and the calculated value
GOLD-CADMIUM
ALLOYS
1147
is thus approximately correct, and suggests strongIy that Kubaschewski’s conclusion (p. 1143) was in error. VII. CONSTITUTION IN THE REGION
AND 25 at.
STRUCTURES
y0 CADMIUM
Owing to the difficulty of obtaining true equilibrium in this region, most of the high-temperature X-ray work was carried out on specimens which had previously been homogenized for 11 weeks at 351°C and were then heated for an hour or more at the required temperature in the X-ray camera before the exposure was started. Other experiments were made with a shorter preliminary anneal and a longer period (up to 48 hr) in the camera. In agreement with previous workers, the a,-phase was found to be face-centred tetragonal, the axial ratio being > 1.0, and decreasing with increasing Cd content. For any given composition, the axial ratio decreases with rise of temperaure, but does not become equal to unity at the (a + a,)/al boundary. The a,-phase boundary limits are shown in Fig. 2,* and on the Cd-rich side the a,-phase extends to about 24 at. % Cd. At slightly higher Cd-contents a f.c.c. phase appears. The high temperature X-ray films could be reconciled with a continuous change from face-centred tetragonal --f f.c.c. with increasing Cd content, but since a change in symmetry is involved, it is probable7 that a S-phase field exists between the tetragonal and cubic phases, and this is confirmed by the fact that the axial ratio/composition data of Owen and Roberts (Zoc.cit.) do not extrapolate to unity inside the al-field. The form of the equilibrium diagram in this region is difficult to establish. Since heavy faulting is present, it may be argued that true thermodynamic equilibrium is never obtained. In this case the region between the f.c.c. and a2 phases should be left as an indefinite field, about 2 at. % in width. In so far as the results of this, and the earlier work may be used, we think that the most probable form of the equilibrium diagram is that of Fig. 2. This is based on more than 100 high-temperature X-ray exposures in the range 20-34 at. % Cd.: Independent work by two of the present authors (V. G. R. and B. R.) using completely different alloys, established the existence of the f.c.c. a,-phase which is shown as undergoing a peritectoidal decomposition at 412°C this temperature being taken from the work * The interplanar spacingsof the a and a, phases are nearly the same and one criterion for a single phase a1 alloy is that the (222) line remains sharp. t We have to thank Dr. J. W. Christian for discussion on this point. $ For clarity of reproduction, the individual points are not shown in Fig. 2.
1148
ACTS
~~ETALLUR~IC~~,
t T
“C
Cadmium
+
Fra. 4. To illustrate a possible form of the equilibrium diagram in the region of 25 at. y0 cadmium. As explained in the text this does not appear to account for all the facts.
Hirabayshi and OgawaQ) on the basis of a carefully determined specific heat~~mperature curve of an alloy oontaining 24 at. a/0Cd, which they regarded as undergoing an order-disorder change, followed by the periteotoidal decomposition. The present authors concluded independently that this transformation is at a lower temperature than the previously accepted value (425%). On the Cd-rich side the existence of a f.c.0. phase suggests another peritectoidal horizontal. This may be placed at 407”C, at which temperature* H. and 0. observed a pronounced narrow peak on their specific heatl~mperature curve. The present results could be reconciled with a diagram of the type of Fig. 4, but this would lead to greater difficulties in interpreting H. and 0.‘~ data. The Cd-rich limit of the new f.c.c. a’ phase is placed at about 25 at. % Cd, in agreement with which 26 at. %Cd alloys prepared from different ingots gave 2-phase (f.c.c. + c.p.h,) diffraction films at the lower temperatures. One nominally 25 at. % Cd alloy gave a f.c. tetragonal diffraction pattern, and it is possible that slight loss of cadmium by volatilization occurred, because another 25 at.‘% Cd alloy gave a f.c.c diffraction pattern with very slight traces of c.p. hexagonal lines. of
DISCUSSION
(a) Liquih
curves of gold a1hy.s with ml&s
ofgroup II
It has previously been pointed out that, in the electrochemical series, gold is more electronegative * H. and 0, interpreted their data as indicating that the alloy in question had crossed a phase-boundary. The pronounced nature of the arrest suggests, however, that it was due to a true latent heat of transformation for which the experimental conditions did not allow an infinite specific heat to be detected.
VOL.
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1962
than copper or silver. The concept of an “eleotrochemical factor” has frequently been used in alloy theory but is difficult to define precisely, because the standard electrode potentials refer to equilibrium between a metal and an aqueous solution of its ions, whilst the Pauling ““electronegativities” are in reality bond energy terms derived from non-metallic compounds. If, as in the Pauling hypothesis (see Pauling’lO)), the metallic bond is regarded as a kind of unsaturated co-valent bond, the Pauling electronegativities are perhaps the least unsatisfactory measure of the ‘~ele~trochemical factor”. Pig. 5 shows the liquidus curves for the alloys of silver and gold with the solutes of group IIB for which the size factors are all favourab1e.t The figure indicates the difference, Ax, between the electronegativities of solvent and solute, and the general effect of increasing Ax in raising the liquidus curves is clear. In the systems Ag- Zn and Au- Zn the size-factor is - 7 per cent (i.e. the solute atom is smaller than that of the solvent) and it may be for this reason that the a-liquidus curves fall relatively steeply in these systems. In the remaining sys~ms the size-factor is very favourable, and the a-liquidus curves for Ag-Mg and Au-Mg fall the least steeply of their respective series. These are the systems with the highest Ax values, and the diagrams suggest that the high electrochemical factor stabilizes the solid phase, presumably by the production of the short-range order. A high electrochemical factor also stabilizes the intermediate solid phases with respect to the liquid. This effect is particularly marked for equiatomic b.c.c. phases with the C&l structure, presumably because each atom is surrounded by 8 of the opposite kind. It is probably because of the great stability of this phase in the systems Au-Mg and Au-&r that closepacked hexagonal phases analogous to the Au-Cd as-phase are not found in these systemsf (b) The cl2close-packed hexagonal phases The characteristic of the a2 close-packed hexagonal phase is the occurrence of severe stacking faulting when the cadmium content is less than about 1 atom in 3. It does not seem possible to account for this on the assumption that, by means of an ordered structure the close-packed hexagonal stacking of spheres can keep the Cd atoms further away from one another than the f.c.c. close-packing, It is possible that Brillouin t A corresponding diagram cannot be drawn for copper, because the size-factors are unfavourable except for CuZn. $ If the free-energy curve of the p phase is sufficiently low, the tangent of this and the f.c.c. curve may pass below the curve for a close-packed hexagonal phase of the a,AuCd type.
RIVLIN,
-.
HUME-ROTHERY
AND
RYDER:
COLD-CADMIUM
b-9
Ax=0.0
Ag-CI
Ax-O.2
Ag-Zn
Ax-O.3
Au- Hq
&u-O5
Au- Cd
Ax-O-7
Au-Zn
Ax-O.8
ALLOYS
Ag-Mq
1149
Ax=0 7
‘\ LX I\ \\ \\
‘--,...
*.-.. FIG. 5. Liquidus
curves of some silver and gold alloys.
zone e&&s may a.ccount for the phenomenon in the following way : It is commonly stated (see Raynor and ~assa~ki(ll)) that with an axial ratio of 1.633 (spherical close packing) a spherical Fermi surface touches the A, B, and C faces of the Jones’ zone (Fig. 6) at electron concentrations of 1.14, 1.36, and 1.67 respectively, but this is incorrect if energy gaps exist, and it is only if such gaps exist that Brillouin zones can exert any effect on alloy structures. The value 1.36 for contact with the B faces is the same as that for contact with the octahedral faces of the first Brillouin zone for the f.c.c. structure, because each corresponds to the same interplanar spacing. But with the close-packed hexagonal structure, the initial contaot with the A faces of the zone means that electron states are cut out, until the zone overlap occurs. The correct statement is, therefore, that: Contact with the A faces of the zone occurs at e.c. 1.14 if the Fermi surface is spherical.
Contact with the B faces occurs at e.c. 1.36 minus an amount which may vary from zero for a zero energy gap at the A faces, to a value corresponding to the volume of 6 spherical caps outside the A faces which have not been occupied because of the energy gaps. Contact of a spherical Fermi surface with the C faces of zone occurs at an electron concentration of 1.67 minus corresponding correction for the effects of the energy gaps at the A and B faces. If the overlap across the A faces occurs before the Fermi surface (assumed spherical) reaches the B faces, the N(E) curve will be of the form of Fig, 7, whereas if the energy gap at the A faces is su~ciently large, the N(E) curve will be of the form of Fig. 8. These curves clearly give the possibility of a region in which the energies of the f.e.c. and close-packed hexagonal structures are nearly the same, whereas with increasing electron concentration the close-packed structure may be stabilized. It does not seem justifiable to speculate further until more is known of the energy gaps and of the distortion of the Fermi surfaces in the alloys.
E
Pm. 6. The
first
Jones’ zone for the hexagonal structure.
close-packed
FIG. 7. Possible X(E) curves for face-centred cubic and close-packed hexagonal structures. For the latter, the energy gaps at the zone faces are assumed to be so small that zone overlaps occur.
1150
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~~ETALLURGICA,
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1962
Oriel College, Oxford, for a research grant. The authors alsoexpress their thanks to the Council of the Royal Society and Imperial Chemical Industries Limited for financial assistance towards the present research. Thanks are also due to Dr. A. Hellawell for much valuable discussion. REFERENCES
E FIU. 8. Possible Nfgf curves for face-centred cubic and close-psoked hexsgonsl structures. For the latter, the energy gaps sre assumed to be so large that no overlapping has occurred while the Fermi surface sprea,ds out to contact with the zone faces at A, B, and C.-The ourves are schematic only, and sre not drswn to scale. ACKNOWLEDGMENTS
One of the authors (V. G. R.) acknowledges with gratitude the award of a D.S.I.R. Research Studentshin, A, whilst another (B. It.) thanks the Fellows of
1. M. RAESEE, Constdt&ioon of Binary Alloys McGEAw-HILL, New York (1958). 2. P. J. DTI’RRANT, J. Inst. MetaL. 41, 139 (1929). 3. 0. KUBASCHEWSEI,Z. p&s. China. 192, 292 (1943). 4. E. A. OWEN and E, A. O’DONNELL R.OBERTS,J. f?a& beak. 66, 389 (1.940). 5. E. A. OWEN and W. H. REES, J. Inst. Metals. 67, 141 (1941). 6. A. BYSTRBMand K. E. ALMIN, Acta them. scmd. 1, ‘76 (1947). 7. M. HIRABAYSRIsnd S. OQAWA, Actu Met. 9, 264 (1961). 8. W. KGSTERand A. SCXNEIDER,2. Metallk. 32, 156 (1940). 9. W. B. PEARSON, Handbook of Lattice i9pacings ad Structures of Metals, Pergamon Press, London (1968). 10. L. PAULINQ, The Nature of the Chemical Bond, Oxford University Press ( 1960). 11. G. V. RAYNOR and T. B. MASS&S~I, Ada Met. 8, 480 (1955).